Drift Transformations of Symmetric Diffusions, and
Duality
Drift Transformations of Symmetric Diffusions, and
Duality
P.J. Fitzsimmons
(To appear in Infinite Dimensional Analysis, Quantum Probability and Related Topics)
Starting with a symmetric Markov diffusion process X (with symmetry measure m and L2(m) infinitesimal generator A) and a suitable core C for the Dirichlet form of X, we describe a class of derivations defined on C. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov's theorem. The transformed process XB is typically non-symmetric, but we are able to show that if the "divergence'' of B is positive, then m is an excessive measure for XB, and the L2(m) infinitesimal generator of XB is an extension of f --> Af+B(f). The methods used are mainly probabilistic, and involve the notions of even and odd continuous additive functionals, and Nakao's stochastic divergence.
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(Version of June 19, 2006)
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June 19, 2006; July 10, 2007
